Package edu.jas.gb

Groebner bases package.

See: Description

Interface Summary

Interface	Description
DReduction<C extends RingElem<C>>	Polynomial D Reduction interface.
EReduction<C extends RingElem<C>>	Polynomial E-Reduction interface.
GroebnerBase<C extends RingElem<C>>	Groebner Bases interface.
PairList<C extends RingElem<C>>	Pair list management interface.
Reduction<C extends RingElem<C>>	Polynomial Reduction interface.
SolvableGroebnerBase<C extends RingElem<C>>	Solvable Groebner Bases interface.
SolvableReduction<C extends RingElem<C>>	Solvable polynomial Reduction interface.
WordGroebnerBase<C extends RingElem<C>>	Non-commutative Groebner Bases interface for GenWordPolynomials.
WordPairList<C extends RingElem<C>>	WordPair list management interface.
WordReduction<C extends RingElem<C>>	Polynomial WordReduction interface.

Class Summary

Class	Description
AbstractPair<C extends RingElem<C>>	Serializable abstract subclass to hold pairs of polynomials.
CriticalPair<C extends RingElem<C>>	Serializable subclass to hold critical pairs of polynomials.
CriticalPairComparator<C extends RingElem<C>>	Comparator for critical pairs of polynomials.
CriticalPairList<C extends RingElem<C>>	Critical pair list management.
DGroebnerBaseSeq<C extends RingElem<C>>	D-Groebner Base sequential algorithm.
DReductionSeq<C extends RingElem<C>>	Polynomial D-Reduction sequential use algorithm.
EGroebnerBaseSeq<C extends RingElem<C>>	E-Groebner Base sequential algorithm.
EReductionSeq<C extends RingElem<C>>	Polynomial E-Reduction sequential use algorithm.
ExtendedGB<C extends RingElem<C>>	Container for a GB and transformation matrices.
GBDist<C extends RingElem<C>>	Deprecated use GroebnerBaseDistributedEC
GBDistHybrid<C extends RingElem<C>>	Deprecated use GroebnerBaseDistributedHybridEC
GBDistSP<C extends RingElem<C>>	Setup to run a distributed GB example.
GBOptimized<C extends GcdRingElem<C>>	Groebner bases via optimized variable and term order.
GBProxy<C extends GcdRingElem<C>>	Groebner bases parallel proxy.
GBTransportMess	Distributed GB transport message.
GroebnerBaseAbstract<C extends RingElem<C>>	Groebner Bases abstract class.
GroebnerBaseDistributed<C extends RingElem<C>>	Deprecated use GroebnerBaseDistributedEC
GroebnerBaseDistributedEC<C extends RingElem<C>>	Groebner Base distributed algorithm.
GroebnerBaseDistributedHybrid<C extends RingElem<C>>	Deprecated use GroebnerBaseDistributedHybridEC
GroebnerBaseDistributedHybridEC<C extends RingElem<C>>	Groebner Base distributed hybrid algorithm.
GroebnerBaseParallel<C extends RingElem<C>>	Groebner Base parallel algortihm.
GroebnerBaseSeq<C extends RingElem<C>>	Groebner Base sequential algorithm.
GroebnerBaseSeqPairDistributed<C extends RingElem<C>>	Groebner Base distributed algorithm.
GroebnerBaseSeqPairParallel<C extends RingElem<C>>	Groebner Base parallel algorithm.
GroebnerBaseSeqPairSeq<C extends RingElem<C>>	Groebner Base sequential algorithm.
Katsura	Class to produce a system of equations as defined by Katsura.
OrderedDPairlist<C extends RingElem<C>>	Pair list management for d-Groebner bases.
OrderedMinPairlist<C extends RingElem<C>>	Pair list management.
OrderedPairlist<C extends RingElem<C>>	Pair list management.
OrderedSyzPairlist<C extends RingElem<C>>	Pair list management.
OrderedWordPairlist<C extends RingElem<C>>	Pair list management of word polynomials.
Pair<C extends RingElem<C>>	Serializable subclass to hold pairs of polynomials.
ReductionAbstract<C extends RingElem<C>>	Polynomial Reduction abstract class.
ReductionPar<C extends RingElem<C>>	Polynomial Reduction parallel usable algorithm.
ReductionSeq<C extends RingElem<C>>	Polynomial Reduction sequential use algorithm.
SolvableExtendedGB<C extends RingElem<C>>	Container for a GB and transformation matrices.
SolvableGroebnerBaseAbstract<C extends RingElem<C>>	Solvable Groebner Bases abstract class.
SolvableGroebnerBaseParallel<C extends RingElem<C>>	Solvable Groebner Base parallel algorithm.
SolvableGroebnerBaseSeq<C extends RingElem<C>>	Solvable Groebner bases sequential algorithms.
SolvableGroebnerBaseSeqPairParallel<C extends RingElem<C>>	Solvable Groebner Base parallel algorithm.
SolvableReductionAbstract<C extends RingElem<C>>	Solvable polynomial Reduction abstract class.
SolvableReductionPar<C extends RingElem<C>>	Solvable polynomial Reduction parallel usable algorithm.
SolvableReductionSeq<C extends RingElem<C>>	Solvable polynomial Reduction algorithm.
WordGroebnerBaseAbstract<C extends RingElem<C>>	Non-commutative Groebner Bases abstract class.
WordGroebnerBaseSeq<C extends RingElem<C>>	Word Groebner Base sequential algorithm.
WordPair<C extends RingElem<C>>	Serializable subclass to hold pairs of word polynomials.
WordReductionAbstract<C extends RingElem<C>>	Polynomial word reduction abstract class.
WordReductionSeq<C extends RingElem<C>>	Polynomial word reduction sequential use algorithm.

Package edu.jas.gb Description

Groebner bases package.

This package contains classes for polynomial and solvable polynomial reduction, Groebner bases and ideal arithmetic as well as thread parallel and distributed versions of Buchbergers algorithm, e.g. ReductionSeq, GroebnerBaseAbstract, GroebnerBaseSeq, GroebnerBaseParallel and GroebnerBaseDistributed. Moreover there are Groebner bases in polynomial rings over principal ideal domains and Euclidean domains, so called D- and E-Groebner bases, see DGroebnerBaseSeq and EGroebnerBaseSeq. The latest additions include free non-commutative polynomial reduction, S-polynomials and two-sided Groebner bases, see WordReductionSeq and WordGroebnerBaseSeq.

Heinz Kredel

Last modified: Fri Sep 21 21:46:36 CEST 2012

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